Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15689563 | C2 | semidirect |
| 2. C22×#13093969 | C2 | semidirect |
| 4. #20252255 | C2 | semidirect |
| 5. #20245453 | C2 | semidirect |
| 6. #20245427 | C2 | semidirect |
| 7. #20245146 | C2 | semidirect |
| 8. #20245103 | C2 | semidirect |
| 9. C47×#2138 | C2 | semidirect |
| 16. C2×#13093970 | C22 | semidirect |
| 19. C2×#13093968 | C22 | semidirect |
| 25. #15689217 | C22 | semidirect |
| 28. Dic47⋊C16 | C22 | semidirect |
| 33. C47×#358 | C22 | semidirect |
| 34. C47×#357 | C22 | semidirect |
| 40. C2×Dic188 | D4 | semidirect |
| 180. #2138 | D47 | semidirect |
| 208. #358 | C2×D47 | semidirect |
| 210. #357 | C2×D47 | semidirect |
| 211. C47 | #33587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689563 | 2 |
| C22×#13093969 | 2 |
| #20253875 | 2 |
| #20252255 | 2 |
| #20245453 | 2 |
| #20245427 | 2 |
| #20245146 | 2 |
| #20245103 | 2 |
| C47×#2138 | 2 |
| #33587 | 47 |